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Journal of Computer Science

Stop Conditions of BB84 Protocol via a Depolarizing Channel (Quantum Cryptography)

Iyed Ben Slimen, Olfa Trabelsi, Houria Rezig, Ridha Bouallà ̈gu, Ammar Bouallègue

Published Jun 1, 2007• 11 citations
Publisher

Abstract

Abstract: BB84 (Bennett and Brassard 1984) is one of the well known protocols of quantum keys distribution. It is built to allow two interlocutors commonly called Alice and Bob to share two similar binary keys and to detect the eavesdropper presence (the eavesdropper is commonly called Eve). However, Eve presence in a disturbed environment causes errors to the sifted keys and decreases the amount of secure information between Alice and Bob. One of the most important stages in BB84 protocol is to decide by using error probability estimation if we can continue the protocol phases or no. Indeed, this decision is function of some factors like: what is the amount of information that we will lose in the error correction phase? What is the degree of errors detected in our sifted keys? What is the origin of these errors: Eve strategy or the channel disturbance? For these reasons, we will study in this study some conditions to stop BB84 protocol in the context of depolarizing channel. We implement two types of eavesdropping strategy: Intercept and Resend and Cloning Attack.

DOI
10.3844/jcssp.2007.424.429

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Cambridge University Press eBooks•Jun 29, 2006•4 citations
Abstract: BB84 (Bennett and Brassard 1984) is one of the well known protocols of quantum keys distribution. It is built to allow two interlocutors commonly called Alice and Bob to share two similar binary keys and to detect the eavesdropper presence (the eavesdropper is commonly called Eve). However, Eve presence in a disturbed environment causes errors to the sifted keys and decreases the amount of secure information between Alice and Bob. One of the most important stages in BB84 protocol is to decide by using error probability estimation if we can continue the protocol phases or no. Indeed, this decision is function of some factors like: what is the amount of information that we will lose in the error correction phase? What is the degree of errors detected in our sifted keys? What is the origin of these errors: Eve strategy or the channel disturbance? For these reasons, we will study in this study some conditions to stop BB84 protocol in the context of depolarizing channel. We implement two types of eavesdropping strategy: Intercept and Resend and Cloning Attack.
The quantum key distribution protocol BB84, published by C. H. Bennett and G. Brassard in 1984, describes how two spatially separated parties can generate a random bit string fully known only to them by transmission of single-qubit quantum states. Any attempt to eavesdrop on the protocol introduces disturbance which can be detected by the legitimate parties. In this Master's Thesis a novel modification to the BB84 protocol is analyzed. Instead of sending single particles one-by-one as in BB84, they are grouped and a non-local transformation is applied to each group before transmission. Each particle is sent to the intended receiver, always delaying the transmission until the receiver has acknowledged the previous particle on an authenticated classical channel, restricting eavesdropping to accessing the quantum transmission one particle at a time. Hence, an eavesdropper cannot undo the non-local transformation perfectly. Even if perfect cloning of quantum states was possible the state of the group could not be cloned. We calculate the maximal information on the established key provided by an intercept-resend attack and the induced disturbance for different transformations. We observe that it is possible to significantly reduce the eavesdropper's maximal information on the key--to one eighth of that in BB84 for a fixed, reasonable amount of disturbance. We also show that the individual access to the particles poses a fundamental restriction to the eavesdropper, and discuss a novel attack type against the proposed protocol.
Problem statement: In a previous research, we investigated the quantum key distribution of the well known BB84 protocol with several intercept and resend attacks.In the present research, we studied the effect of many eavesdroppers cloning attacks of the Bennett-Brassard cryptographic protocol on the quantum error and mutual information between honest parties and information with sender for each eavesdropper.Approach: The quantum error and the mutual information were calculated analytically and computed for arbitrary number of cloning attacks.Our objective in this study was to know if the number of the eavesdroppers and their angle of cloning act on the safety of information.Results: It was found that the quantum error and the secured/no secured transition depend strongly on the number of eavesdropper and their angle of attacks.The particular cases where all eavesdroppers collaborate were also investigated.Conclusion: Furthermore, the cloning attack's quantum error is lower than the intercept and resends attacks one, which means that the cloning attacks is the optimal one for arbitrary number of eavesdropper.
Quantum Key Distribution (QKD) provides an innovative approach for secure communication by utilizing the principles of quantum mechanics. Among various QKD protocols, the BB84 protocol remains the most widely studied and implemented due to its simplicity and theoretical security guarantees. However, practical implementations of BB84 are vulnerable to several eavesdropping attacks and channel imperfections. This paper presents a comprehensive study on the detection and analysis of eavesdropping attacks in the BB84 protocol. The work focuses on common attacks such as intercept-resend attack, photon-number splitting attack, Trojan horse attack, and phase-covariant cloning attack. The effect of these attacks on Quantum Bit Error Rate (QBER) is analyzed in detail. Simulation-based observations are discussed to demonstrate how QBER increases under malicious interference. The study further explores statistical methods for detecting eavesdropping and examines practical countermeasures including decoy states, privacy amplification, and error correction techniques. The paper concludes that BB84 remains robust against eavesdropping when proper detection and mitigation mechanisms are employed.
The goal of the protocol QKD BB84 is to allow a transmitter and a receiver which uses a quantum channel to exchange their keys and to detect the presence of eavesdropping attacks. In the present research, we investigate the effect of several eavesdroppers with both intercept-resend and cloning attacks. We will propose the different possible cases of the positioning of the eavesdroppers and their strategies of attacks; also we will calculate the mutual information for each case. The explicit expressions of the mutual information and quantum error clearly show that the security of the exchanged information depends on the numbers of the eavesdroppers and their attacks parameters on the quantum channel.
The publication of the BB84 protocol by Bennett and Brassard in 1984 [10] marks the beginning of quantum key distribution. Since then, many other protocols have been invented. Yet, BB84 keeps a privileged place in the list of existing protocols: it is the one most analyzed and most often implemented, including those used in commercial products, e.g., [91, 113]. In this chapter, I define the BB84 protocol, although I already described it informally in Section 1.1. The physical implementation is then investigated. Finally, I analyze the eavesdropping strategies against BB84 and deduce the secret key rate. Description Alice chooses binary key elements randomly and independently, denoted by the random variable X ∈ χ = {0, 1}. In this protocol, there are two encoding rules, numbered by i ∈ {1, 2}. Alice randomly and independently chooses which encoding rule she uses for each key element. In case 1, Alice prepares a qubit from the basis {|0〉, |1〉} as In case 2, Alice prepares a qubit from the basis {|+〉, |−〉} as On his side, Bob measures either Z or X , yielding the result Y Z or Y X , choosing at random which observable he measures. After sending a predefined number of qubits, Alice reveals to Bob the encoding rule for each of them. They proceed with sifting, that is, they discard the key elements for which Alice used case 1 (or case 2) and Bob measured Z (or X ). For the remaining (sifted) key elements, we denote Bob's sifted measurements by Y .